Question 1115916
You start the same way as if normal base-ten numbers division:
<pre>

       __________________________________________
2x-3   |    8x^3     -6x^2     -7x     +1
       |
       |

</pre>


The entire process:
<pre>
             4x^2      3x       1
       __________________________________________
2x-3   |    8x^3     -6x^2     -7x     +1
       |
       |    8x^3     -12x^2
        --------------------
            0         6x^2    -7x
                      6x^2   -9x
                     --------------
                       0      2x    +1
                              2x   -3
                              -----------
                              0     4
</pre>

QUOTIENT:   {{{4x^2+3x+1}}}  
REMAINDER:   {{{4}}}


MEANING:   {{{4x^2+3x+1+4/(2x-3)}}}